standard form

Learning Objective:

• we are learning to write numbers using standard form

Investing:

• This is useful because it helps us to write large and small numbers in a useful way.
• A functional (real-life) application is we may need to work with large distances in outer space:.
  • See NASA for information on space exploration
  • See CERN for information about the Large Hadron Collider
• Very small numbers are also used in science to describe the tiny distances or times involved in chemistry, biology, physics and electrical engineering:
  • the size of a virus
  • the length of a molecule
  • the mass of a nutrino or life span of an unstable particle
  • the size of a transistor on a modern microchip

Preparing:

• Watch these videos to see why standard form is useful...

• and another:

Discovering:

• A googol is the digit 1 followed by 100 zeros. This is so large I don't want to type it!
• It can be written in standard index form as:

$\ 1 \times 10^{100}$

Modeling:

• Here are some examples of people getting it right:

$\ 1450000 = \ 1.45 \times 10^{6}$
$\ 0.000987 = \ 9.87 \times 10^{-4}$
$\ 23400000 = \ 2.34 \times 10^{7}$

• Here are some examples of people getting it wrong:

$\ 12000 = \ 12 \times 10^{3}$
$\ 0.0073 = \ 0.73 \times 10^{-2}$

• Can you explain why the examples above are wrong? How do we decide if numbers are in standard form?

Practicing:

• Use this widget to change numbers to standard form.

• Work with a partner to complete these tarsia jigsaws to see if you can change between standard form and ordinary numbers and carry out calculations.

Standard Form jigsaw large numbers.fjsw

• Details
• Download
• 19 KB

Standard Form jigsaw small numbers.fjsw

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• 21 KB

Standard Form jigsaw calculations.fjsw

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• 36 KB

Standard Form jigsaw calculations.fjsw

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• Download
• 36 KB

Assessing:

• Could you create a poster explaining standard form?

last edited: Jan 21, 2012 3:42 pm